Developing the Self-Calibrating Palmer Drought Severity Index Is this computer science or climatology? Steve Goddard Computer Science & Engineering, UNL

Oct. 26 th, 2007Computer Science & Engineering, UNL Outline 1. What is Drought? 2. The PDSI 3. Self-Calibrating the PDSI 4. Summary

Oct. 26 th, 2007Computer Science & Engineering, UNL What is Drought?

Oct. 26 th, 2007Computer Science & Engineering, UNL What is the PDSI? The PDSI is a drought index that models the moisture content in the soil using a supply and demand model. Is an accumulating index Developed during the early 1960’s by W. C. Palmer, published in Designed to allow for comparisons over time and space.

Oct. 26 th, 2007Computer Science & Engineering, UNL Where is it used?

Oct. 26 th, 2007Computer Science & Engineering, UNL How is it calculated? LatitudeTemperatureAverage Temp Estimate Moisture Demand Moisture Departure Estimate Potential Evapotranspiration Available Water Holding Capacity Precipitation Subtract

Oct. 26 th, 2007Computer Science & Engineering, UNL How is it calculated? Moisture Departure Weighting process Weighted Combination Moisture Anomaly Previous PDSI Duration Factors Climatic Characteristic Current PDSI

Oct. 26 th, 2007Computer Science & Engineering, UNL Problems with the PDSI

Oct. 26 th, 2007Computer Science & Engineering, UNL Step 1: Supply  Demand More Detail on PDSI Calculations

Oct. 26 th, 2007Computer Science & Engineering, UNL Moisture Departure: d The moisture departure represents the excess or shortage of moisture. The same value of d may have a different effect at different places, as well as at different times. –Examples: A shortage of 1” will matter more during the growing season than during winter. An excess of 1” will be more important in a desert region than in a region that historically receives several inches of rain each month.

Oct. 26 th, 2007Computer Science & Engineering, UNL Step 2: Adjustment The moisture departure, d, is adjusted according to the climate and time of year to produce what is called the Moisture Anomaly, which is symbolized as Z. Z is the significance of d relative to the climate of the location and time of year. Z is calculated by multiplying d by K, which is called the Climatic Characteristic.

Oct. 26 th, 2007Computer Science & Engineering, UNL Climatic Characteristic: K K is calculated as follows: where

Oct. 26 th, 2007Computer Science & Engineering, UNL Step 3: Combine with Existing Trend The PDSI is calculated using the moisture anomaly as follows: The values of and 1/3 are empirical constants derived by Palmer, and are called the Duration Factors. They affect the sensitivity of the index to precipitation events.

Oct. 26 th, 2007Computer Science & Engineering, UNL Self-Calibration Improving the spatial and temporal resolution of the index requires automatic calibration of: Duration Factors Climatic Characteristic

Oct. 26 th, 2007Computer Science & Engineering, UNL Duration Factors The Duration Factors are the values of and 1/3 that are used to calculate the PDSI. They affect the sensitivity of the index to precipitation as well as the lack of precipitation.

Oct. 26 th, 2007Computer Science & Engineering, UNL Duration Factors - from Palmer Palmer calculated his duration factors by examining the relationship between the driest periods of time and the ΣZ over those periods.

Oct. 26 th, 2007Computer Science & Engineering, UNL Duration Factors - from Palmer The equation for this linear relationship is: Let b = and m = Then the duration factors can be found as follows:

Oct. 26 th, 2007Computer Science & Engineering, UNL Duration Factors - Wet and Dry Most locations respond differently to a deficiency of moisture and an excess of moisture. Calculate separate duration factors for wet and dry periods by repeating Palmer’s process and examining extremely wet periods.

Oct. 26 th, 2007Computer Science & Engineering, UNL Duration Factors - Automated Example from Madrid, NE

Oct. 26 th, 2007Computer Science & Engineering, UNL Climatic Characteristic The climatic characteristic adjusts d so that it is comparable between different time periods and different locations. The resulting value is the Moisture Anomaly, or the Z-index. This process can be broken up into two steps.

Oct. 26 th, 2007Computer Science & Engineering, UNL The first step adjusts the moisture departure for comparisons between different time periods. Climatic Characteristic - Step 1

Oct. 26 th, 2007Computer Science & Engineering, UNL Climatic Characteristic - Step 2 The second step adjusts for comparisons between different regions. Edwards Plateau, Texas Southern Texas Western Kansas Texas High Plains Western Tennessee West Central Ohio Central Iowa Scranton, Pennsylvania Northwestern North Dakota

Oct. 26 th, 2007Computer Science & Engineering, UNL Climatic Characteristic - Redefinition All of the problems with the Climatic Characteristic come from Step 2. What does this ratio really represent?

Oct. 26 th, 2007Computer Science & Engineering, UNL Now what? Climatic Characteristic - Redefinition

Oct. 26 th, 2007Computer Science & Engineering, UNL Answer: use the relationship between the ∑Z and the PDSI Climatic Characteristic - Redefinition

Oct. 26 th, 2007Computer Science & Engineering, UNL What is the “expected average” PDSI? If there is one, it would be zero. Now what? Climatic Characteristic - Redefinition

Oct. 26 th, 2007Computer Science & Engineering, UNL Besides zero, what other benchmarks does the PDSI have? Answer: A user would expect “extreme” values to be extremely rare. The only other benchmarks are the maximum and minimum of the range. Climatic Characteristic - Redefinition From a user’s point of view, what are the expected characteristics of the PDSI?

Oct. 26 th, 2007Computer Science & Engineering, UNL If extreme values are truly going to be considered extreme, they should occur at the same low frequency everywhere. What should this frequency be? –There should be one extreme drought per generation. Frequency of extreme droughts about 2% 12 months of extreme drought every 50 years. Climatic Characteristic - Redefinition

Oct. 26 th, 2007Computer Science & Engineering, UNL Consider both extremely wet and dry periods: –To make the lowest 2% of the PDSI values fall below -4.00, map the 2 nd percentile to –To make the highest 2% of the PDSI values fall above +4.00, map the 98 th percentile to Climatic Characteristic - Redefinition

Oct. 26 th, 2007Computer Science & Engineering, UNL Climatic Characteristic - Final Redefinition Wait a second…. Isn’t K used to calculate the PDSI? How can the PDSI be used to calculate K?

Oct. 26 th, 2007Computer Science & Engineering, UNL Calibration Technique

Oct. 26 th, 2007Computer Science & Engineering, UNL Calibration Technique - Summary –Dynamically calculate the duration factors, following Palmer’s method and adjusting for poor correlation and abnormal precipitation. –Redefine the climatic characteristic to achieve a regular frequency of extremely wet and dry readings by mapping the 2 nd percentile to and the 98 th to +4.00

Oct. 26 th, 2007Computer Science & Engineering, UNL Calibration Technique Effects: –The index is now calibrated for both wet and dry periods. –Almost all stations have about the same frequency of extreme values. –The same basic algorithm can be used to calculate a PDSI over multiple time periods.

Oct. 26 th, 2007Computer Science & Engineering, UNL Multiple Time Periods Why? –To more easily correlate the PDSI with another type of climate data such as tree rings, or satellite data. Valid monthly periods are divisors of 12: –Single month, 2-month, 3-month, 4-month, 6-month. Valid weekly periods are divisors of 52: –Single week, 2-week, 4-week, 13-week, 26-week.

Oct. 26 th, 2007Computer Science & Engineering, UNL Analysis How do we evaluate the Self-Calibrated PDSI? –Best way Try to correlate the Self-Calibrated PDSI to actual conditions. –Easy way Simply compare the Self-Calibrated PDSI to the original PDSI. –Computer Science way: Write a few number-crunching scripts to do the work; performing any number of statistical examinations of the Self-Calibrated PDSI.

Oct. 26 th, 2007Computer Science & Engineering, UNL Statistical Analysis What to look for in the statistical analysis. –Frequency of extreme values –Stations that are wet more often than dry and vice versa. –Average range of PDSI values

Oct. 26 th, 2007Computer Science & Engineering, UNL Statistical Analysis Original Monthly Self- Calibrating Monthly Self- Calibrating Weekly (max + min) > 1.0 The maximum PDSI value was significantly higher than the minimum was low %16.03%16.67% (max + min) < -1.0 The minimum PDSI value was significantly lower than the maximum was high %1.92%4.49% The frequency with which extremely wet PDSI values (above 4.00) was between 1% and 3% 13.46%91.03% The frequency with which extremely dry PDSI values (below -4.00) was between 1% and 3% 2.56%87.82% Range was greater than %0.00% Range was greater than %1.92%3.28% Range was greater than %52.56%65.38% Range was greater than %99.36%100.00%

Oct. 26 th, 2007Computer Science & Engineering, UNL Spatial Analysis Percent of time the PDSI and SC-PDSI are at or above 4.0

Oct. 26 th, 2007Computer Science & Engineering, UNL Spatial Analysis Percent of time the PDSI and SC-PDSI are at or below -4.0

Oct. 26 th, 2007Computer Science & Engineering, UNL Conclusion The SC-PDSI is now used throughout the world. Increased spatial and temporal resolution than feasible with PDSI. It is more spatially comparable than PDSI Performs the way we believe Palmer meant his drought index to perform, and the way he would have implemented it if computers were as readily available as they are today. Well, that is what we tell the climatologist anyway…

Oct. 26 th, 2007Computer Science & Engineering, UNL Questions